Is it 2 different questions or just one?
Answer:
- 0.5 + 2.985i
- 1 + 2.828i
- 1.5 + 2.598i
- 2 + 2.236i
Explanation:
Complex numbers have the general form a + bi, where a is the real part and b is the imaginary part.
Since, the numbers are neither purely imaginary nor purely real a ≠ 0 and b ≠ 0.
The absolute value of a complex number is its distance to the origin (0,0), so you use Pythagorean theorem to calculate the absolute value. Calling it |C|, that is:
Then, the work consists in finding pairs (a,b) for which:
You can do it by setting any arbitrary value less than 3 to a or b and solving for the other:
![\sqrt{a^2+b^2}=3\\ \\ a^2+b^2=3^2\\ \\ a^2=9-b^2\\ \\ a=\sqrt{9-b^2}](https://tex.z-dn.net/?f=%5Csqrt%7Ba%5E2%2Bb%5E2%7D%3D3%5C%5C%20%5C%5C%20a%5E2%2Bb%5E2%3D3%5E2%5C%5C%20%5C%5C%20a%5E2%3D9-b%5E2%5C%5C%20%5C%5C%20a%3D%5Csqrt%7B9-b%5E2%7D)
I will use b =0.5, b = 1, b = 1.5, b = 2
![b=0.5;a=\sqrt{9-0.5^2}=2.958\\ \\b=1;a=\sqrt{9-1^2}=2.828\\ \\b=1.5;a=\sqrt{9-1.5^2}=2.598\\ \\b=2;a=\sqrt{9-2^2}=2.236](https://tex.z-dn.net/?f=b%3D0.5%3Ba%3D%5Csqrt%7B9-0.5%5E2%7D%3D2.958%5C%5C%20%5C%5Cb%3D1%3Ba%3D%5Csqrt%7B9-1%5E2%7D%3D2.828%5C%5C%20%5C%5Cb%3D1.5%3Ba%3D%5Csqrt%7B9-1.5%5E2%7D%3D2.598%5C%5C%20%5C%5Cb%3D2%3Ba%3D%5Csqrt%7B9-2%5E2%7D%3D2.236)
Then, four distinct complex numbers that have an absolute value of 3 are:
- 0.5 + 2.985i
- 1 + 2.828i
- 1.5 + 2.598i
- 2 + 2.236i
Answer:
plug in the numbers for radius, and know your formulas. a diameter is 2 times a radius so
Pi or 3.14 times D is the same as 2 times pi times radius.
Option B
I think its opinion B because its cheaper